Gen 1: Red, albeit that my parents only let me rent it, and after I played so much on it, they wouldn't actually buy a Gameboy for me. I only got stuck at around the third Gym before it had to be returned. I now have my own Red version that a friend gave me, but the save file won't last 24 hours, so the internal battery must be dead. I have never finished a Gen I game, and it looks like I never will.
Gen 2: Silver.
I don't remember the exact details, but I believe it was because someone else who played Pokemon that I befriended was going to get Gold, but it might have only been on a whim. I played that game for many hours on end, and remember getting my Typhlosion and Politoed into the 90s, though I can't check, seeing as how the save file went poof. Same thing went for my Crystal version.
Gen 3: Sapphire.
I think partially because the box art was blue, which was closer to my first game's silver coloration than Ruby's, so I choose Sapphire out of tradition, and because I liked Kyogre better. Emerald however had more of the things that I thought that Sapphire lacked (namely animated sprites and being able to catch Pokemon not found in the Hoenn 'Dex).
FR/LG: Neither, due to being perfectly and contently busy with Emerald, even though I had planned to get one, and even got the guide book. And unless either appears on my doorstep, or I manage to both do every single starship design that I can think of, and IV train an example of each and every Pokemon there is, as well as IV breed every competitive set there is, or otherwise run out of things to keep me occupied, I get the feeling it just isn't going to happen. Besides, there is no Johto for me to return to!
Gen 4: Diamond
Again, Diamond's box color was blue, so I choose that out of tradition, and I liked Dialga better anyways. It helped that a friend that I made who also played Pokemon decided to choose Pearl. Once again, I liked Platinum even better, due to the Battle Frontier and being able to catch even more Pokemon.
HG/SS: Soul Silver
I was really looking forward to this, as Silver was my very first game, and so I figured why not let history repeat itself? It helped that my friend Patrick chose to get HeartGold. And indeed, Soul Silver was one of the funnest of the series I've ever played. In comparison, White was a bit of a disappointment, but I forced myself to stop playing SoulSilver eventually, seeing as how it was now obsolete, and that was no longer where the competitive battles were.
Gen V: White
I mostly choose White because I liked Zekrom better of the two, and the fact that it just so happened that he was in the White version was even better, because the choice of choosing Black or White could also be seen as a philosophical choice of choosing between dark and light, and I naturally choose the light side.
B2/W2: Neither, and that was a choice that I regret. Pokestar Studios looked fun, and if not for Pokedit, I would have never gotten a Genesect. At the time, I was busy with college, wasn't playing Pokemon very much, and in fact didn't even use the Dream World when it first opened. I don't think I had even beaten the Elite Four at the time B2/W2 came out, so I saw no reason to get either of them, seeing as how I wasn't playing White very much. B2/W2 was the only time in a Generation after Gen II that I didn't get a second version.
Gen 6: Y
I liked Yvetal better, plain and simple. Normally, I'd go for the version with the blue on the box art, but not this time. If they go the B2/W2 route again, I'll probably get X2.
OR/AS: Alpha Sapphire
Once again, a case of allowing history to repeat itself, and what better way to see how the games had changed from the original? Besides, I think Kyogre looks more majestic than the hunched over Groudon, who looks like his back is aching, as opposed to the proud, tall stance of Tyranitar or the predatory stance of Tyrantrum.